Solving Min Vertex Cover with Iterated Hopfield Networks

  • A. Bertoni
  • P. Campadelli
  • G. Grossi
Conference paper
Part of the Perspectives in Neural Computing book series (PERSPECT.NEURAL)

Abstract

A neural approximation algorithm for the Min Vertex Cover problem is designed and analyzed. This algorithm, having in input a graphs G = (V, E), constructs a sequence of Hopfield networks such that the attractor of the last one represents a minimal vertex cover of G. We prove a theoretical upper bound to the sequence length and experimentally compare on random graphs the performances (quality of solutions, computation time) of the algorithm with those of other known heuristics. The experiments show that the quality of the solutions found by the neural algorithm is quite satisfactory.

Keywords

Min Vertex Cover Hopfield networks approximation algorithms 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A. Bertoni, P. Campadelli, and G. Grossi. A neural algorithm for the maximum clique problem: Analysis, experiments and circuit implementation. Algoritmica. (To appear).Google Scholar
  2. 2.
    M. R. Garey and D. S. Johnson. Computers and Intractability. A Guide to the Theory of NP-Completeness. W. H. Freeman k Co., San Francisco, CA, 1979.MATHGoogle Scholar
  3. 3.
    F. Gavril. Quoted in [2], pag. 134.Google Scholar
  4. 4.
    J. Håstad. Some optimal inapproximability results. In M. Sipser, editor, Proceedings of the 29th ACM Symposium on the Theory of Computation, pages 1–10, New York, NY, 1997. ACM Press.Google Scholar
  5. 5.
    J. J. Hopfield. Neural networks and physical systems with emergent collective computational abilities. Proceedings of the National Academy of Sciences of the United States of America, 79(8):2554–2558, 1982.MathSciNetCrossRefGoogle Scholar
  6. 6.
    A. Jagota. Approximating maximum clique with a Hopfield network. Technical Report 92–33, Department of Computer Science, SUNY Buffalo, December 1992.Google Scholar
  7. 7.
    R. M. Karp. Reducibility among Combinatorial Problems, pages 85–103. Complexity of Computer Computations. Plenum Press, New York, 1972.Google Scholar
  8. 8.
    Clarkson K. L. A modification of the greedy algorithm for vertex cover. Information Processing Letters, (16):23–25, 1983.MathSciNetCrossRefGoogle Scholar
  9. 9.
    Bar-Yehuda R. and S. Even. A local-ratio theorem for approximating the weighted vertex cover problem. Annals of Discrete Mathematics, (25):27–45, 1985.MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2002

Authors and Affiliations

  • A. Bertoni
    • 1
  • P. Campadelli
    • 1
  • G. Grossi
    • 1
  1. 1.Dipartimento di Scienze dell’InformazioneUniversità degli Studi di MilanoMilanoItaly

Personalised recommendations